Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T08:42:02.241Z Has data issue: false hasContentIssue false
  • English
  • Français

On separable cyclic extensions of rings

Published online by Cambridge University Press:  09 April 2009

George Szeto  and
Yuen-Fat Wong
George Szeto
Affiliation:
Department of Mathematics, Bradley University, Peoria, Illinois 61625, U.S.A.
Yuen-Fat Wong
Affiliation:
Department of Mathematics, DePaul University, Chicago, Illinois 60637, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The quaternion algebra of degree 2 over a commutative ring as defined by S. Parimala and R. Sridharan is generalized to a separable cyclic extension B[j] of degree n over a noncommutative ring B. A characterization of such an extension is given, and a relation between Azumaya algebras and Galois extensions for B[j] is also obtained.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 2 , April 1982 , pp. 165 - 170
Copyright
Copyright © Australian Mathematical Society 1982

References

Auslander, M. and Goldman, O. (1960), ‘The Brauer group of a commutative ring,’ Trans. Amer. Math. Soc. 97, 367–409.CrossRefGoogle Scholar
Chase, S. U., Harrison, D. K. and Rosenberg, A. (1965), ‘Galois theory and Galois cohomology of commutative rings,’ Mem. Amer. Math. Soc. Soc. 52.Google Scholar
Frank, DeMeyer (1966), ‘Galois theory in separable algebras over commutative rings,’ Illinois J. Math. 2, 287–295.Google Scholar
Frank, DeMeyer and Edward, Ingraham (1971), Separable algebras over commutative rings, Lecture notes in Mathematics 181 (Springer-Verlag, Berlin-Heidelberg-New York).Google Scholar
Parimala, S. and Sridharan, R. (1977), ‘Projective modules over quaternion algebras,’ J. Pure Appl. Algebra, 9, 181–193.CrossRefGoogle Scholar
Szeto, G. (1980), ‘A characterization of a cyclic Galois extensions of commutative rings,’ J. Pure Appl. Algebra, 16, 315–322.CrossRefGoogle Scholar
Szeto, G. and Wong, Y. F. (to appear), ‘On free quadratic extensions of rings’.Google Scholar